How to Find the Prime Factors and Factor Pairs of 143
The concept of factors of 143 is essential in mathematics and helps in solving real-world and exam-level problems efficiently. Mastering factors is especially useful in topics like divisibility, prime factorization, and finding GCF/LCM, which are all important for competitive and board exams.
Understanding Factors of 143
A factor of 143 is any whole number that divides 143 exactly, leaving no remainder. Understanding the factors of 143 is widely used in number theory, divisibility rules, and prime factorization. It also helps in comparing composite and prime numbers, and is a vital foundation for higher maths topics like LCM and HCF.
How to Find the Factors of 143
To find the factors of 143, start by dividing 143 by all numbers between 1 and 143. If your division leaves a remainder of zero, then that number is a factor. Let’s go step-by-step:
1. 143 ÷ 1 = 143
2. 143 ÷ 11 = 13
3. 143 ÷ 13 = 11
4. 143 ÷ 143 = 1
So, the factors of 143 are 1, 11, 13, and 143.
Prime Factorization of 143
Prime factorization is expressing a number as a product of its prime factors. Here’s how you can write 143 as a product of primes:
1. 143 is an odd number so it's not divisible by 2.
2. Check divisibility by 3, 5, and 7 (none divide 143).
3. Try 11: 143 ÷ 11 = 13. Both 11 and 13 are prime numbers.
Therefore, the prime factorization of 143 = 11 × 13.
Factors of 143 in Pairs
Pair factors are two numbers that multiply to give 143. Here is a clear table showing them:
Factors of 143 – Pair Table
| Factor 1 | Factor 2 |
|---|---|
| 1 | 143 |
| 11 | 13 |
Therefore, the pair factors of 143 are (1, 143) and (11, 13).
Properties and Divisibility of 143
143 is an odd, composite number (not prime). It is not a perfect square, as the square root of 143 (~11.96) is not a whole number. Its only prime factors are 11 and 13. It is not divisible by numbers like 2, 3, 5, or 7.
Related Numbers and Their Factors
Exploring numbers close to 143 can deepen understanding. For example, 91 (factors: 1, 7, 13, 91), 144 (factors: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144). You can practice factorization using such examples for exams and further revision. For prime numbers and deeper divisibility techniques, explore Prime Numbers and Fundamental Theorem of Arithmetic.
Worked Example – Solving a Problem
1. Find the sum of all factors of 143.
2. Is 143 a perfect square?
3. What is the greatest common factor (GCF) of 143 and 156?
So, GCF is 13
Practice Problems
- List all factors of 143 by the division method.
- Write the prime factorization of 143.
- Is 143 a prime or composite number?
- What are the pair factors of 143?
- Find the LCM of 143 and 11.
Common Mistakes to Avoid
- Forgetting to check factors beyond 10 (like 11 and 13, both factor 143).
- Confusing factors (numbers that divide) with multiples (numbers you get by multiplying).
- Assuming 143 is a perfect square or prime without checking the definition.
Real-World Applications
The concept of factors of 143 and similar numbers appears in practical scenarios such as arranging objects in equal groups, dividing items evenly, encryption algorithms, and problem-solving in exams. Vedantu helps students link these core maths concepts to real-life and higher studies.
We explored the idea of factors of 143, how to find them, their prime factorization, pair factors, common mistakes, and their real-life relevance. With regular practice on Vedantu, you can gain complete confidence in such maths concepts for both school and competitive exams.
Explore more and practice with these related topics: Factors of 91, Factors of 144, Factors of 100, Prime Numbers, Common Factors, Fundamental Theorem of Arithmetic, Factors of a Number, Multiples of 4.
FAQs on What Are the Factors of 143?
1. What are the factors of 143?
The factors of 143 are the numbers that divide 143 exactly without leaving a remainder. These are 1, 11, 13, and 143.
2. Is 143 a prime number?
No, 143 is not a prime number. It is a composite number because it has more than two factors: 1, 11, 13, and 143.
3. What is the prime factorization of 143?
The prime factorization of 143 is the expression of 143 as a product of its prime factors. For 143, it is 11 × 13, where both 11 and 13 are prime numbers.
4. How do you find the factors of 143 by division method?
To find the factors of 143 by the division method, divide 143 by all natural numbers starting from 1 up to 143. Whenever the division leaves no remainder, the divisor is a factor. For example: 143 ÷ 1 = 143, 143 ÷ 11 = 13, 143 ÷ 13 = 11, and 143 ÷ 143 = 1, so the factors are 1, 11, 13, and 143.
5. What are the common multiples of 143?
The common multiples of 143 are multiples shared with other numbers. The first few multiples of 143 are 143, 286, 429, 572, 715, 858, 1001, 1144, 1287, and 1430. To find common multiples between 143 and another number, look for numbers that appear in both their multiples lists.
6. Is 143 a perfect square?
No, 143 is not a perfect square because its square root is not an integer. The square root of 143 is approximately 11.96, which means it cannot be expressed as the square of a whole number.
7. Why is 143 not divisible by 2 or 5?
143 is not divisible by 2 or 5 because it does not satisfy their divisibility rules. It is not an even number (does not end with 0, 2, 4, 6, or 8), so it is not divisible by 2. Also, it does not end with 0 or 5, so it cannot be divided evenly by 5.
8. Why do students confuse factors of 143 with its multiples?
Students often confuse factors and multiples because both relate to division and multiplication. Factors are numbers that divide 143 exactly, while multiples are numbers obtained by multiplying 143 by whole numbers. Understanding this distinction helps in topics like divisibility and number theory.
9. Can the factors of 143 help in finding LCM or HCF with other numbers?
Yes, knowing the factors of 143 is useful in calculating the HCF (Highest Common Factor) and LCM (Least Common Multiple) when combined with other numbers. For example, the factors help identify common factors for HCF and prime factors for calculating LCM efficiently.
10. What makes 143 a composite, not a prime number?
143 is composite because it has more than two factors. A prime number has exactly two factors: 1 and itself. Since 143 can be divided exactly by 1, 11, 13, and 143, it meets the composite number definition.
11. Does 143 appear as a factor in standard math tables or competitive exams?
Yes, 143 and its factors commonly appear in board exams and competitive exams especially in questions on divisibility, factors, multiples, HCF, and LCM. Knowing the factors of 143 helps students solve arithmetic and number theory problems efficiently.
